Which of the following numbers is a factor of 161? ${3,7,8,9,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $161$ by each of our answer choices. $161 \div 3 = 53\text{ R }2$ $161 \div 7 = 23$ $161 \div 8 = 20\text{ R }1$ $161 \div 9 = 17\text{ R }8$ $161 \div 14 = 11\text{ R }7$ The only answer choice that divides into $161$ with no remainder is $7$ $ 23$ $7$ $161$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $161$ $161 = 7\times23 7 = 7$ Therefore the only factor of $161$ out of our choices is $7$. We can say that $161$ is divisible by $7$.